Angular correlations between unidentified charged trigger (t) and associated (a) particles are measured by the ALICE experiment in Pb-Pb collisions at sqrt(sNN) = 2.76 TeV for transverse momenta 0.25 < pT^{t,a} < 15 GeV/c, where pT^t > pT^a. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval |\eta| < 1.0. Distributions in relative azimuth \Delta\phi \equiv \phi^t - \phi^a are analyzed for |\Delta\eta| \equiv |\eta^t - \eta^a| > 0.8, and are referred to as "long-range correlations". Fourier components V_{n\Delta} \equiv <cos(n\Delta\phi)> are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy V_{n\Delta}(pT^t, pT^a) is fully described in terms of single-particle anisotropies v_n(pT) as V_{n\Delta}(pT^t, pT^a) = v_n(pT^t) v_n(pT^a). This expectation is tested for 1 \leq n \leq 5 by applying a global fit of all V_{n\Delta}(pT^t, pT^a) to obtain the best values v_n{GF}(pT). It is found that for 2 \leq n \leq 5, the fit agrees well with data up to pT^a \sim 3-4 GeV/c, with a trend of increasing deviation as pT^t and pT^a are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full 0.25 < pT < 15 GeV/c range using a single v_n(pT) curve; such a description is however approximately possible for 2 \leq n \leq 5 when pT^a < 4 GeV/c. For the n=1 harmonic, however, a single v_1(pT) curve is not obtained even within the reduced range pT^a < 4 GeV/c.